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|a Tabuada, Gonçalo
|e author
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|a Massachusetts Institute of Technology. Department of Mathematics
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|a Noncommutative motives in positive characteristic and their applications
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|b Elsevier BV,
|c 2020-07-14T17:38:02Z.
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|z Get fulltext
|u https://hdl.handle.net/1721.1/126181
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|a Let k be a base field of positive characteristic. Making use of topological periodic cyclic homology, we start by proving that the category of noncommutative numerical motives overkis abelian semi-simple, as conjecturedby Kontsevich. Then, we establish a far-reaching noncommutative generaliza-tion of the Weil conjectures, originally proved by Dwork andGrothendieck. Inthe same vein, we establish a far-reaching noncommutative generalization of the cohomological interpretations of the Hasse-Weil zeta function, originallyproven by Hesselholt. As a third main result, we prove that the numericalGrothendieck group of every smooth proper dg category is a finitely generatedfree abelian group, as claimed (without proof) by Kuznetsov. Then, we introduce the noncommutative motivic Galois (super-)groupsand, following aninsight of Kontsevich, relate them to their classical commutative counterparts.Finally, we explain how the motivic measure induced by Berthelot's rigid cohomology can be recovered from the theory of noncommutativemotives.
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|a en
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|a Article
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|t 10.1016/J.AIM.2019.04.020
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|t Advances in mathematics
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